Phase-based optical interferometric techniques are widely employed in optical distance measurements in which sub-wavelength distance sensitivity is required. Optical distance is defined as the product of the refractive index and the length. However, most such techniques are limited by an issue which is widely known in the filed at 2π ambiguity or integer ambiguity which can be defined as the difficulty in telling the interference fringes of an axial scan apart from each other. An unmodified harmonic phase based low coherence interferometry (LCI) method can be used to determine the differential optical distance, (nλ2−nλ1)L, where L is the physical distance, nλ1 and nλ2 are the refractive indices at the wavelengths λ1 and λ1, respectively, if the optical distance is increased gradually so that the differential phase measured by LCI can be tracked through its 2π wrap over. To determine (nλ2−nλ1) for DNA in solution, for example, the DNA concentration is gradually increased in the measuring cuvette. While such a measurement approach works well in a controlled environment, it can hardly be implemented in a situation where there is less manipulability in the sample. For example, the method does not work on a fixed slab of material which one is constrained to keep whole.
The problem lies in the fact that unmodified LCI is unable to tell the interference fringes of an axial scan apart from each other, described herein as the 2π ambiguity issue. It is a problem that plagues most phase-based optical interferometric techniques. As a result, these techniques are unable to determine optical distance absolutely. Therefore, most such techniques are used in applications, such as evaluating the texture of continuous surfaces or detecting time-dependent distance changes, in which phase unwrapping is possible through comparison of phases between adjacent points or over small time increments.
In many applications it is important to quantitatively measure the phase of light transmitted through or reflected from a sample. In particular, the phase of light transmitted through or reflected from biological samples can form a powerful probe of structure and function in living or nonliving cells.
Interferometry is a versatile technique for measuring the phase of light. One common problem in quantitative interferometry is the susceptibility to phase noise due to external perturbations such as vibrations, air motions, and thermal drafts. There remains a need for systems for phase measurement which solve the problem of phase noise.
Interferometry is one way to access the phase information associated with a specimen. Techniques such as phase contrast and Nomarski microscopy use optical phase just as a contrast agent and do not provide quantitative information about its magnitude. Several techniques exist for measuring the phase of light transmitted through nearly transparent samples. These include digital recorded interference microscopy (DRIMAPS) and noninterferometric detection of phase profiles via the transport of intensity equation.
Reflection interferometry is capable of sensitivity much smaller than the wavelength of light used. Measurements on the scale of fractions of nanometers or smaller are common in metrology and microstructure characterization. However, little work has been done in nanometer-scale interferometry in weakly reflecting samples such as biological cells and tissues. Optical coherence tomography (OCT), an interferometric technique used with biological samples, is primarily concerned with the amplitude rather than the phase of interference from reflected light, and is therefore limited in resolution to the coherence length of the light used, typically 2-20 microns.
Phase-referenced reflection interferometry has been used to measure the volume changes in a monolayer of cells. The harmonic phase-based interferometer used requires two sources, is relatively slow (5 Hz), and has a phase sensitivity of about 20 mrad over this bandwidth. There thus remains a need for effective systems for phase measurement which solve the problem of phase noise and assist in developing different imaging applications.